The Capitals had rallied from a three-goal deficit during the final 22 minutes of regulation, but Bonino’s second goal of the playoffs sent the Penguins to the Eastern Conference finals against Tampa Bay.

Holtby made the initial stop on Carl Hagelin, but Bonino, camped right outside the crease, tapped in the winner.

Washington forward Jay Beagle made a remarkable save from his belly against Patric Hornqvist early in overtime, but there was no stopping Bonino’s tap-in.

Phil Kessel scored twice, and Hagelin added a goal for Pittsburgh.

The rookie Matt Murray made 36 saves as the Penguins continued their playoff mastery over the Capitals.

T. J. Oshie, Justin Williams and John Carlson scored during Washington’s rally, but it was not enough.

Nine times the longtime rivals have met in the playoffs. Eight times the post-series handshake line has ended with Pittsburgh celebrating while Washington trudges toward the off-season.

The Capitals, who won the Presidents’ Trophy for having the N.H.L.’s best regular-season record, avoided elimination with a solid 3-1 win in Game 5, but the Penguins — who squandered 3-1 series leads in the 2011 and 2014 playoffs — preached patience and pointed to their remarkable resilience under Coach Mike Sullivan, who took over in mid-December.

Pittsburgh ended the regular season as the hottest team in the league and has now won two playoff rounds by relying on the depth that General Manager Jim Rutherford has cultivated behind the stars Sidney Crosby and Evgeni Malkin.

All but two of Pittsburgh’s 16 goals during the series were scored by players who were not on the roster when Rutherford replaced Ray Shero two summers ago, including Kessel, acquired from Toronto last July, along with Hagelin and Bonino, Pittsburgh’s best line in the series.

Correction:

An earlier version of this article misstated the number of goals the Penguins scored in the series. It was 16, not 15.

A version of this article appears in print on , on Page B10 of the New York edition with the headline: Penguins Score in Overtime, Ending Capitals’ Run. Order Reprints | Today’s Paper | Subscribe